A Numerical Study of the Temperature Reduction by Water Spray Systems within Urban Street Canyons

To reduce energy demand (both fossil fuel and renewable energy) for cooling the urban heat island environment, some solutions have been studied. Among these methods, the water spray system is considered more flexible due to its dynamic controls. This study investigated the cooling effect of water spray systems in the street canyon under different aspect ratios and high relative humidity environments using a computational fluid dynamics model. This model was validated with water channel and wind tunnel experiments. The results showed that the most effective cooling area was the area just under the spray nozzles. However, in a narrow street canyon, people in the middle of the street may feel the cooling effect because of the dispersion and accumulation of the cooled air. Our simulations demonstrated that air under the nozzles was saturated and this revealed that under drier conditions the water spray systems will have higher cooling performance. We also found that using large water droplets created a wider cooling area in the middle of the street canyon, and this phenomenon was not changed much if the nozzle height was increased from 2.5 m to 3.5 m.


Introduction
The urban heat island forms as a result of urbanization and energy consumption (both fossil fuel and renewable energy). It affects urban micrometeorology [1] and aggravates climate change, which has increased the frequency and intensity of heat waves [2], and will then rapidly increase energy demand by 70% for air conditioning during the whole 2000-2100 period [3].
Some adaptations have been confirmed as valid for cooling urban areas or buildings, such as green walls, green ponds [4], roof ponds [5], vegetation, increase of short wave reflectivity, and water spray systems. Among these, the water spray system is considered more flexible with its dynamic controls in warm seasons while passive cooling systems such as vegetation and increase in short wave reflectivity also reduce temperature in all seasons. The water spray system is also an energy efficient, economical, and environmentally friendly method for improving thermal comfort in urban environments [6,7]. Reducing energy consumption for thermal comfort can then lead mitigate climate change (and urban heat island) and form a positive feedback loop for energy demand, climate change, and heat waves relations.
Furthermore, experiments conducted by Jain and Rao (1974) [8] showed that roof water spray systems performed better in reducing ceiling temperature than roof ponds did (15 • C and 13 • C, respectively). Huang et al., (2011) [9] conducted several experiments and proved that the water spray system is very effective since it reduced temperature by 5-7 • C under an ambient temperature of 35 • C and a relative humidity of 45%. In spite of these benefits and universal applications, studies on the cooling effect of water spray systems in urban environments are found to be relatively rare.
Numerical simulation by a Computational Fluid Dynamics (CFD) model is a tool suitable for studying momentum, energy, and particle flows since it is more efficient and cheaper than full-scale measurements and wind-tunnel experiments. However, the interaction between water droplets and air is rather complicated since it is a two-phase flow, which takes into account the effect of energy exchange when droplets evaporate, as well as momentum exchange between droplets and air flow. In order to simulate these effects, the Lagrangian-Eulerian model separates a two-phase flow into the discrete phase part (Lagrangian model) and continuous phase part (Eulerian model), and these two models are coupled during the simulation. Several validation studies with small-scale and full-scale experimental data showed that the Lagrangian-Eulerian model is reliable for simulating the two-phase flow [6,10].
Although the Lagrangian-Eulerian model is widely used to simulate the two-phase flow, there are only a few studies applying this model to urban environments. Montazeri et al., (2017) [7] simulated a water spray system in an urban landscape using the Lagrangian-Eulerian approach. The results showed that for a water spray system installed at a height of 3 m with a water mass flow rate of 0.15 kg/s and under relative humidity of around 30%, a temperature reduction of approximately 7 • C was found at the height of 1.75 m in the courtyard, and thus heat stress was alleviated efficiently. However, the study only simulated the cooling effect in a specific courtyard with fixed meteorological conditions. With different building geometry or meteorological conditions (e.g., relative humidity), the cooling effect may be quite different.
An urban street canyon is the space between buildings that line up continuously along both sides of a relatively narrow urban street. The wind velocity field [11] and pollutants dispersion [12] in urban street canyons have been studied. They concluded that the aspect ratio (building height divided by street width) is a crucial parameter that affects the velocity field and the dispersion of pollutants in the street canyon, in which more pollutants would be trapped in a street canyon with a higher aspect ratio. This phenomenon is likely to influence the outcome of the cooling effect within street canyons, since the cooling effect is affected by the dispersion of water droplets. The water spray system is widely used to reduce air temperature in the urban canyons in residential-commercial mixed areas and night markets in South Asian cities (e.g., Taipei) during summers. Moreover, most of the residential-commercial mixed areas and night markets in Taipei are built in street canyons with aspect ratios larger than 1, which means that the wind velocity would be small in this region. With a high population density, low wind speed, and high temperature in the summer, there is a high demand for using the water spray system to reduce temperatures in the street canyons. However, this cooling effect has not yet been studied in a numerical manner. In order to contribute a wider application of the water spray system, this study applied the Lagrangian-Eulerian model to simulate the cooling effect of water spray systems in the urban street canyon with manipulation of four variables: (1) the aspect ratio of the street canyon; (2) the relative humidity; (3) water droplet size; and (4) the height of the spray nozzle.

Computational Geometry and Grids
The computational geometry was a 3D long street canyon with building height, H; street width, W; and street length, L; where L was set to be much larger than H. Three types of street canyon, with the aspect ratio H/W = 1, 2, and 3, respectively, were considered in this study ( Figure 1); these aspect ratios (H/W) mimic the general street canyons of residential-commercial mixed areas in Taipei city, Taiwan. As shown in Figure 1, the vertical (z direction) computational domain size was two times that of the building height; the building width was the same as the building height. Following Baik and Kim (1999) [11], the horizontal (x direction) domain size was equal to two times that of the building width plus the street width. The street widths (W) were 15, 10, and 5 m for H/W = 1, 2, and 3, respectively. The street lengths (L) were all fixed to be 150 m for the three street canyons. In terms of meshing the computational domains, uneven grid sizes were adopted; the grids inside the street canyon were set to be finer than those on the outside; the grid size of cells adjacent to the buildings and street were also set to be finer to model the effect of building boundaries. The grid sizes and numbers for the three street canyons were determined with the convergence test on the horizontal velocity. Based on the tests, the number of grids were 295,075, 241,100, and 305,350 for H/W = 1, 2, and 3, respectively. The results of meshing for these three street canyons were shown in Figure 2.

Numerical Scheme
All of the calculations were performed with ANSYS FLUENT [13]. The Eulerian part of the Lagrangian-Eulerian model contains continuous phases such as flow velocity field, temperature field, and vapor concentration field. These were solved with 3D Reynolds-Averaged Navier-Stokes equations combined with the energy equation (see Appendix A). Closure was obtained by the Re-Normalization Group (RNG) k-ε model. The model validation by Chan et al., (2002) [12] suggested the RNG k-ε model is an optimum model (compared to the standard k-ε model) and a realizable model when simulating the flow field in a street canyon. In this study, pressure-velocity coupling was performed with the Semi-Implicit Method for Pressure Linked Equations (SIMPLE). Second-order discretization schemes were used for all convection and viscous terms and second-order implicit time integration was used for the temporal discretization. Note that second-order implicit time integration could avoid the sharp temperature reduction caused by the accumulation of droplets when a large velocity gradient occurs.
The Lagrangian part of the Lagrangian-Eulerian model, including discrete phases such as velocity, temperature, and mass of water droplets (see Appendix B) were solved with the discrete phase model (DPM) implemented by the ANSYS FLUENT. In this model, particles were accelerated by the drag (spherical drag law) and gravity forces.
The time step of the continuous phase was 0.05 s, 15 iterations per time step; also, the particle time step was 0.001 s and 20 iterations were done for each DPM calculation. All of the time step sizes were determined with convergence tests.

Boundary Conditions
The leftmost boundary was an air flow inlet boundary and the boundary conditions for inlet flow velocity, kinetic energy (k), and kinetic energy dissipation rate (ε) were set as the following [11]: where U i is the inlet horizontal flow velocity in x direction, W i is the vertical velocity at the inlet boundary and assumed to be zero, U r (=4 m/s) is the velocity at the computational boundary top (=2H), κ is the von Kármán constant (=0.4), C µ is a constant (=0.0845), and z' is the vertical distance from the top of the buildings. The buildings and street were thermal adiabatic, and standard wall function [14] were applied. The roughness height (k s ) and roughness constant (C s ) of the building boundaries were set to be non-zero to model the effect of roughness of the boundaries, where k s = 9.793 z o /C s , and z o is roughness length. Roughness heights of these boundaries were all set to be 1.5; the roughness constants were set to be 0.5 by the validation in Section 3.1.
A model considering the interaction between the boundary and the discrete phase was needed. Since the temperature of the boundaries is below the boiling point of water, the "wall jet" boundary condition was not needed [13]. This study assumed that the water droplets would be trapped on the wall, and the effect of the water film on the wall was neglected; thus an "escape" boundary condition in ANSYS FLUENT discrete particle model was set so that water droplets would disappear when they touch the wall.

Water Spray Nozzle and Droplet Characteristics
In this study, a cone spray nozzle model provided by ANSYS FLUENT 16.2 was adopted. The half-cone angle (α/2) was 20 degrees, the radius was 2 mm, and the total number of droplet streams was 15, i.e., there were 15 injection points which were uniformly placed on the perimeter of the spray nozzle. In the simulation, two sets of nozzles were placed in the street canyon, each set consisted of 7 nozzles. In each nozzle set, the distance between two adjacent nozzles follows the setting of Montazeri (2017) [7], which was 0.5 m. The 7 nozzles were installed in the same x and z coordinates, and the y coordinates were 0, ±0.5, ±1.0, ±1.5 m, respectively. Each nozzle set was placed 1 m away from the building wall in the street canyon (see Figure 3). The water droplet size is important since it affects the drag force, gravity force, and the residence time in the flow field. In this study, we considered small and large mean water droplet diameters (D), which were 20 and 369 µm, respectively. For the cases with D = 20 µm, the minimum (D min ) and maximum (D max ) diameters of water particles were 10 and 60 µm, respectively; the mass flow rate of water ( . m) from each nozzle was 0.01 kg/s; the velocity of water droplet (V w ) was −15 m/s. For the cases with D = 369 µm, D min and D max were 74 and 518 µm, respectively; . m was 0.2 kg/s and V w was −22 m/s. The water droplet size distribution was determined by the Rosin-Rammler model [15] and the spread parameter, n, was 3.5 [7]. Ten discrete droplet diameters, D n , were assumed to be injected from each droplet stream into the air. The 10 droplet diameters were distributed evenly between D min and D max , i.e., the interval was (D max − D min )/D n . The mass and number distribution of different diameters of water droplets in the two cases (D = 20 and 369 µm) were plotted in Figures 4 and 5, respectively. The temperature of water droplets was 25 • C and each injection of water spray lasted for 0.05 s. All of the common CFD and nozzle characteristic parameters used in this study were also summarized in Table 1, and heat exchange between air and water droplets, considering the effect of latent heat loss by water evaporation, is also described in Appendix C.

Cooling Effect Simulation Cases
To study the effects of the aspect ratio of the urban street canyon, relative humidity, water droplet size, and the height of the spray nozzle, three group simulations were conducted and summarized in Table 2. H/W is the aspect ratio of street canyon, RH is relative humidity, V w is the velocity of water droplet, . m is the water mass flow rate, D is the mean particle size of water droplets, D min and D max are the minimum and maximum particle sizes of water droplets, respectively, and h s is the height of the nozzle.

Validation of the Flow Field in Urban Street Canyon
Baik et al., (2000) [16] studied the urban street canyon flow using a circulating water channel; they published the measured vertical velocity profiles in the street canyon with the aspect ratio of 1 and 2; they also compared their measurements with the simulation results using the numerical model by Baik and Kim (1999) [11]. In this study, we validated our model simulations of the flow field by the experimental measurements of Baik et al., (2000) [16] and the model predictions by Baik and Kim (1999) [11]. The measured and predicted vertical profiles of the normalized vertical and horizontal velocities at the upstream (x/W = 0.125), middle (x/W = 0.5), and downstream (x/W = 0.875) positions with H/W = 1 and H/W = 2 were presented in Figures 6 and 7, respectively. The linear regression and root mean square error (RMSE) of vertical and horizontal velocities between the experimental data and model predictions by Baik and Kim (1999) [11] and present study were also summarized in Tables 3 and 4, respectively. In the case of H/W = 1, for both vertical and horizontal velocities, our simulations fitted well with the experiments. In the case of H/W = 2, the comparisons were not as good as those of H/W = 1 but were still reasonable. Figures 6 and 7 and Tables 3 and 4 demonstrated that the simulated flow fields by this study for the street canyons of H/W = 1 and 2 were reasonable.  [16]; dash line denotes the prediction by Baik and Kim (1999) [11]; solid line denotes the prediction by this study.

Evaporation Cooling Validation
The cooling effect validation of the 3D steady RNG k-ε model, coupled with steady DPM in ANSYS FLUENT, was based on the wind tunnel experiments by   [17]. In the experiment, a hollow-cone nozzle spray was installed in the middle of the inlet of the wind tunnel, and 9 wet bulb temperature (WBT) meters and dry bulb temperature (DBT) meters were installed on the outlet of the wind tunnel. The x, y, and z dimensions of the test section in the wind tunnel experiment by Sureshkumar   For validating the present model, we selected the case where the inlet velocity was 3 m/s and the DBT and WBT of inlet air were 39.2 and 18.7 • C, respectively. The characteristics of the water droplets were: T w = 35.2 • C, V w = −22.05 m/s, . m = 0.208 kg/s, D = 369 µm, D min = 74 µm, D max = 518 µm, spread parameter n = 3.67. The half-cone angle (α/2) was 18 • and the radius of the spray nozzle was 2 mm.
The DBT and specific humidity predictions by this study were compared with the wind tunnel experimental data and plotted in Figure 9. Errors of DBT were all within 10% of the measurements and errors of specific humidity were around 10-30%. These error ranges were reasonable and similar to the predictions of Sureshkumar et al., (2008) [18].  Figure 10 shows the velocity fields in the street canyon before and after the spray nozzles operated for RH = 70% and H/W = 1 (Case 1.1). Figures 11 and 12 are the same as Figure 10 but for H/W = 2 (Case 2.1) and H/W = 3 (Case3.1), respectively. From Figures 10-12, we noticed that in the street canyons of H/W = 2 and 3, after the operation of spray systems, the wind velocity fields near the ground were mainly affected by the streams of spray nozzles rather than the wind flowing into the street canyon from outside. Similar results were also observed by Moureh and Yataghene (2016) [19], where the air curtain induced surrounded air flows. This implies that the water spray system (i.e., spray nozzle and water droplet size) would influence the cooling effect in the street canyon as well as the air flow. To further examine the flow field in the street canyon, we plotted the vertical profiles of normalized horizontal velocity (u) and vertical velocity (w) at the middle point (x/W = 0.5, y = 0) before and after spray systems operated for H/W = 1, 2, and 3 in Figures 13-15, respectively. These figures showed that, at the middle point of the street canyon, after the operation of spray nozzles, the horizontal and vertical velocities only changed slightly due to the air flow induced by water spray. Figure 16 shows the temperature contours on the plane: y = 0 for Case 1.   Figure 19. Two distinct regions were noticed in Figure 17, Figure 18, and Figure 19: the region between the nozzle set and the building wall (first region) and the street canyon region between the two nozzle sets (second region). For clarity purposes, the first (I) and second (II) regions were labeled on Figure 18c only. From Figure 19, in region I, just under the nozzles, the air temperature dropped dramatically for all the cases, and reached around the theoretically lowest temperature, which was the wet bulb temperature (discussed later). In region II, regardless of whether there was a condition of RH = 70% or 80%, the cooling effect in cases of H/W = 3 (Case 3.1 and 3.2) were the most efficient (largest temperature drops); cases of H/W = 1 (Case 1.1 and 1.2) were the second; and cases of H/W = 2 (Case 2.1 and 2.2) were the third. The fact that cases of H/W = 1 were better than cases of H/W = 2 was because the air velocity in H/W = 1 was faster. The reason that cases of H/W = 3 had the best cooling performance was due to having the narrowest street canyon.          Table 5. For H/W = 1 and 2, it is clear that the cooling effect is not much (temperature drops between 0.39 to 1.25 • C only) in region II due to a wider street canyon and/or lower air velocity. Figure 19 and Table 5 revealed that the water spray system could only cool the area under the nozzle sets unless the street canyon was narrow.  Also, from Table 5, when the relative humidity changed from 80 to 70%, the average temperature reductions of region II for H/W = 1, 2, and 3 were 0.41, 0.31, and 1.35 • C, respectively. In other words, for region II, when the air is drier, the water spray system could cool the air more only for the cases where the street canyon is narrow. For region I, when the air is drier (RH changed from 80 to 70%), the water spray system could reduce the air temperature more by 1.73, 1.43, and 1.45 • C for H/W = 1, 2, and 3, respectively.  Figure 21 is the same as Figure 20 but for Cases 2.2 (small particle, RH = 80%) and 2.2a (large particle, RH = 80%). In Case 2.1, the lowest temperature of the cooled air was about 30 • C, while in Case 2.1a, the lowest temperature was also around 30 • C. However, most of the cooled air in Case 2.1 accumulated at the very bottom of the street canyon. In Case 2.1a, because of the larger velocity of wind caused by the large water droplets from the nozzles, the cooled air in the middle of the street canyon could spread wider (though the cooled air at the very bottom was not saturated by the water droplets). In Figure 21, comparison between Case 2.2 (small particle, RH = 80%) and 2.2a (large particle, RH = 80%) showed similar results as those in Figure 20, but the cooled air in the middle of the street canyon was also saturated by the water droplets in Case 2.2a. This demonstrated that under high humidity conditions (RH ≥ 80%), even large water droplets could saturate the air at the very bottom as the small particles did. The benefit of using large particles was that the cooling area was wider.

Effects of Water Droplet Size and Height of Spray Nozzles
Comparison between Figures 20 and 21 suggested that the cooling effect was better when spraying large water droplets into the air than small ones. This was due to the larger velocity and water mass flow rate caused by the large water droplets.  When the air is saturated with water vapor, the air temperature will reach the lowest bound, which is the wet bulb temperature (see Appendix C). Hence, the wet bulb temperature provides an analytical solution of the lowest temperature that the evaporating cooling could reach by spraying water droplets into air. Table 6 lists the wet bulb temperatures solved by Equations (A15) and (A16) under 60, 70, and 80% relative humidity conditions. From Table 6, it is clear that under drier conditions and higher background air temperature, the cooling effect by water spray systems is better. In this study we also investigated the effect of nozzle height on cooling with large water droplets. Figure 22 shows the temperature contours on the plane: y = 0 for Case 2.1a (h s = 2.5 m, D = 369 µm), Case 2.1b (h s = 3.0 m, D = 369 µm), and 2.1c (h s = 3.5 m, D = 369 µm). Comparison in Figure 22 reveals that when the nozzle height was increased (from 2.5 to 3.5 m), the cooling area in the middle of the street canyon was reduced but the reductions in air temperature were about the same. To further examine the cooling effect by increasing the nozzle height, we plotted the horizontal temperature profiles in x-direction at y = 0 and z = 1.5 m for Case 2.1a (h s = 2.5 m), Case 2.1b (h s = 3.0 m), and Case 2.1c (h s = 3.5 m) in Figure 23. For comparison purpose, Case 2.1 (h s = 2.5 m, small water droplets) was also shown in Figure 23. Notice that for all the three large particle cases, the air just under the nozzles at height = 1.5 m all became saturated. However, the temperature differences among these cases at height = 1.5 m were small because the air was almost saturated at this height. This indicated that increasing the nozzle height would not increase the cooling effect at the height of 1.5 m. Figure 23 also demonstrated that using large water droplets has better cooling performance than using the small ones (Case 2.1a vs. Case 2.1).

Conclusions
This study simulated the cooling effect of water spray systems in the urban street canyon using the Computational Fluid Dynamics (CFD) method. The 3D unsteady k-ε model coupled with discrete phase model (DPM) provided by ANSYS FLUENT was adopted. The model validation was carried out by flow fields of the urban street canyon measured in water channel experiments [16] and by temperature fields of the wind tunnel experiments [17].
The finding of this study can improve the efficiency of using water spray systems for reducing temperature under different climate conditions and reduce energy demand (including renewable energy) for air conditioning in residential and commercial areas under climate change.
By our simulation results, we conclude the following: (1) Under region I, the cooling effects were about the same (with a difference of around 1 • C) for different aspect ratios. For region II, H/W = 3 had the best cooling performance, H/W = 1 was the second, and H/W was the third. (2) Relative humidity has significant influence on the cooling performance. The drier the air, the better the cooling performance of the water spray system is. (3) The cooling effect was better when spraying large water droplets into the air than small ones.
This was due to the larger velocity and water mass flow rate caused by the large water droplets. (4) Increasing the nozzle height (from 2.5 to 3.5 m) would not increase the cooling effect at the height of 1.5 m.
In summary, if the street width is large (W = 10 or 15 m), the cooled area is just under the spray nozzle. If the street is narrow (W = 5 m), people in the middle of the street also feel the cooling effect.
To extend the application of water spray systems for improving thermal comfort under hot weather (especially in heat waves), future work should focus on how water spray systems would work in wide open areas (e.g., parks, play grounds, outdoor food courts). Understanding the cooling effect of water spray systems with manipulation of other controlling variables, like nozzle spray angle, ambient wind velocity, and incoming radiation, is also needed.
β is the thermal expansion coefficient in the form: 1/ρ (∂ρ/∂T). η = Sk/ , Sk is the scalar measure of the deformation tensor, η 0 and a are 4.38 and 0.012, respectively, and C 2 = 1.68. Water vapor mass conservation: where D m is molecular diffusivity (m 2 /s), D t is turbulent diffusivity (m 2 /s), which can be obtained by Sc t = ν t D t , where Sc t (=0.7) is the turbulent Schmidt number. S v is the source term due to the evaporation of the droplet in discrete particle model. Energy conservation equation: where Pr t (turbulent Prandtl number) is 0.85, S h is source term which is contributed by latent heat absorbed during the evaporation of droplets. E is total energy of the fluid (J/kg/m 3 ) defined as: vapor concentration in the air (mol/m 3 ). K c is calculated from the empirical correlation of Sherwood number [21]: Sh = k c d p D = 2 + 0.6·Re 0.5 ·Sc 0.33 (A12) where Sh is the Sherwood number; D is the diffusion coefficient of vapor (m 2 /s); Sc is the Schmidt number, which is given as: Sc = µ/ρD.
(3) Particle heat transfer: where C pw is the specific heat of water droplet (J/kg), λ is the latent heat of water (kJ/mol), h is the convection heat transfer coefficient, which was calculated from the empirical correlation of Nu number when vapor mass fraction << 1 [22]: where k a is the thermal conductivity of the continuous phase, Pr is the Prandtl number of the continuous phase, which is given as: Pr = c p µ/k a .